The 27-year-old Englishman hit six birdies to remain in strong contention at the midway point, tied with Xander Schauffele and Pat Perez, the latter of whom bogied on the last to miss out on a share of top spot.
A group of five others are two shots behind, including Rory McIlroy - two-under for the day - as the Northern Irishman seeks his first major in four years.
Elsewhere, defending champion Jordan Spieth managed a second-round 67 to climb to three-under for the tournament.
THE OPEN LEADERBOARD AFTER ROUND 2
1. Zach Johnson (-6)
2. Kevin Kisner (-6)
3. Tommy Fleetwood (-5)
4. Pat Perez (-5)
5. Xander Schaufefele (-5)